Finite Group Databasebeta

← C151×#24384 #50329309

Subgroups — C151×#24384 #50329309

Order 38656.

1970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic, complemented
2C2×#469×C151C212yesmaximal, complemented
3C2×#447×C151C211yesmaximal, characteristic, complemented
4C2×#407×C151C211yesmaximal, characteristic, complemented
5#2847×C151C211yesmaximal, characteristic, complemented
6#2034×C151C212yesmaximal, complemented
7#1999×C151C212yesmaximal, complemented
8#1895×C151C212yesmaximal, complemented
9#1874×C151C211yesmaximal, characteristic, complemented
10#1853×C151C211yesmaximal, characteristic, complemented
11#1786×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151—21no—
13C23×D4×C151C2211yescharacteristic
14C24×C4×C151C2211yescharacteristic
15C22×D8×C151C2212yescomplemented
16C22×M16×C151C2212yescomplemented
17C2×#121×C151—21no—
18C2×#121×C151—21no—
19C2×#121×C151—28no—
20C2×#121×C151C2211yescharacteristic
21C2×#121×C151C2212yes—
22C2×#121×C151C2212yes—
23C2×#121×C151C2211yescharacteristic, complemented
24C2×#121×C151C2211yescharacteristic, complemented
25C2×#120×C151—21no—
26C22×C4⋊C4×C151C2211yescharacteristic
27C22×C22⋊C4×C151—21no—
28#469×C151—28no—
29#447×C151—24no—
30C2×#106×C151C2212yescomplemented
31C2×#102×C151C2212yescomplemented
32C2×#102×C151C2212yescomplemented
33C2×#102×C151C2212yescomplemented
34C2×#102×C151C2212yescomplemented
35#407×C151—24no—
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2212yescomplemented
39#386×C151—21no—
40#386×C151—21no—
41#386×C151—21no—
42#380×C151C2211yescharacteristic
43#380×C151C2211yescharacteristic, complemented
44#380×C151C2211yescharacteristic, complemented
45#340×C151C2212yescomplemented
46#340×C151C2212yescomplemented
47C25×C151—21no—
48C25×C151D411yescharacteristic
49C22×D4×C151—28no—
50C22×D4×C151—24no—
51C22×D4×C151—21no—
52C22×D4×C151—22no—
53C22×D4×C151—22no—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151—21no—
57C22×D4×C151—22no—
58C22×D4×C151—22no—
59C22×D4×C151—44no—
60C22×D4×C151—44no—
61C22×D4×C151—42no—
62C22×D4×C151C2311yescharacteristic
63C22×D4×C151C2312yes—
64C23×C4×C151—22no—
65C23×C4×C151—24no—
66C23×C4×C151—22no—
67C23×C4×C151—21no—
68C23×C4×C151—42no—
69C23×C4×C151D411yescharacteristic
70C23×C4×C151D411yescharacteristic
71C23×C4×C151D411yescharacteristic
72C23×C4×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C2×D8×C151—24no—
76C2×D8×C151—24no—
77C2×D8×C151—42no—
78C2×M16×C151—24no—
79C2×M16×C151—24no—
80C2×M16×C151—42no—
81C22×C8×C151C2312yes—
82C22×C8×C151C2312yes—
83#121×C151—28no—
84#121×C151—28no—
85#121×C151—24no—
86#121×C151—24no—
87#121×C151—24no—
88#121×C151—22no—
89#121×C151—24no—
90#121×C151—22no—
91#121×C151—42no—
92#121×C151D418yescomplemented
93#120×C151—44no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—24no—
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2312yes—
100C2×C22⋊C4×C151—28no—
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109#106×C151—24no—
110#102×C151—24no—
111#102×C151—24no—
112#102×C151—24no—
113#102×C151—42no—
114C22⋊C8×C151—22no—
115C22⋊C8×C151—24no—
116C22⋊C8×C151D414yescomplemented
117#95×C151—21no—
118#95×C151—21no—
119#95×C151—21no—
120C24×C151—22no—
121C24×C151—22no—
122C24×C151—22no—
123C24×C151—24no—
124C24×C151—22no—
125C24×C151—22no—
126C24×C151—22no—
127C24×C151—21no—
128C24×C151—41no—
129C24×C151—41no—
130C24×C151—42no—
131C24×C151—42no—
132C24×C151—42no—
133C24×C151—42no—
134C24×C151—42no—
135C24×C151—42no—
136C24×C151C2×D411yescharacteristic
137C24×C151C2×D411yescharacteristic
138C24×C151C2×D411yescharacteristic
139C2×D4×C151—24no—
140C2×D4×C151—28no—
141C2×D4×C151—28no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—21no—
146C2×D4×C151—22no—
147C2×D4×C151—21no—
148C2×D4×C151—22no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—48no—
152C2×D4×C151—48no—
153C2×D4×C151—42no—
154C2×D4×C151—432no—
155C2×D4×C151—44no—
156C2×D4×C151—44no—
157C2×D4×C151—44no—
158C2×D4×C151—44no—
159C2×D4×C151—42no—
160C2×D4×C151—42no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151C2×D414yes—
170C22×C4×C151—22no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—24no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—22no—
179C22×C4×C151—22no—
180C22×C4×C151—22no—
181C22×C4×C151—22no—
182C22×C4×C151—22no—
183C22×C4×C151—21no—
184C22×C4×C151—22no—
185C22×C4×C151—21no—
186C22×C4×C151—22no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—41no—
191C22×C4×C151—41no—
192C22×C4×C151—41no—
193C22×C4×C151—48no—
194C22×C4×C151—48no—
195C22×C4×C151—42no—
196C22×C4×C151—42no—
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D414yes—
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D412yes—
202C22×C4×C151#4112yes—
203C22×C4×C151C2411yescharacteristic
204D8×C151—48no—
205M16×C151—48no—
206C2×C8×C151—22no—
207C2×C8×C151—22no—
208C2×C8×C151—22no—
209C2×C8×C151—22no—
210C2×C8×C151—22no—
211C2×C8×C151C2×D414yescomplemented
212C4⋊C4×C151—24no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151C2×D414yes—
219C22⋊C4×C151—28no—
220C22⋊C4×C151—28no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—28no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—24no—
245C23×C151—44no—
246C23×C151—44no—
247C23×C151—44no—
248C23×C151—44no—
249C23×C151—44no—
250C23×C151—48no—
251C23×C151—48no—
252C23×C151—48no—
253C23×C151—44no—
254C23×C151—42no—
255C23×C151—42no—
256C23×C151—42no—
257C23×C151—42no—
258C23×C151—42no—
259C23×C151—42no—
260C23×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—84no—
268C23×C151—84no—
269C23×C151—84no—
270C23×C151—84no—
271C23×C151#12012yes—
272C23×C151#12112yes—
273C23×C151AGL(1,ℤ/8)12yes—
274C23×C151AGL(1,ℤ/8)12yes—
275C23×C151AGL(1,ℤ/8)12yes—
276C23×C151C22×D411yescharacteristic
277D4×C151—24no—
278D4×C151—24no—
279D4×C151—48no—
280D4×C151—416no—
281D4×C151—416no—
282D4×C151—42no—
283D4×C151—42no—
284D4×C151—42no—
285D4×C151—42no—
286D4×C151—84no—
287D4×C151—84no—
288D4×C151—84no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—24no—
294C2×C4×C151—24no—
295C2×C4×C151—24no—
296C2×C4×C151—24no—
297C2×C4×C151—21no—
298C2×C4×C151—24no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—44no—
302C2×C4×C151—44no—
303C2×C4×C151—44no—
304C2×C4×C151—48no—
305C2×C4×C151—42no—
306C2×C4×C151—42no—
307C2×C4×C151—42no—
308C2×C4×C151—42no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151#12012yes—
319C2×C4×C151#12112yes—
320C2×C4×C151C22×D411yescharacteristic
321C2×C4×C151C22×D412yes—
322C2×C4×C151C2×#4111yescharacteristic
323C2×C4×C151H(5,𝔽2)12yes—
324C8×C151—24no—
325C8×C151—42no—
326C22×C151—22no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—22no—
331C22×C151—22no—
332C22×C151—22no—
333C22×C151—22no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—22no—
337C22×C151—22no—
338C22×C151—416no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—44no—
348C22×C151—44no—
349C22×C151—44no—
350C22×C151—816no—
351C22×C151—82no—
352C22×C151—82no—
353C22×C151—82no—
354C22×C151—82no—
355C22×C151—81no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151—81no—
359C22×C151—81no—
360C22×C151—81no—
361C22×C151—81no—
362C22×C151#46914yescomplemented
363C22×C151C2×#12011yescharacteristic
364C22×C151C2×#12111yescharacteristic
365C22×C151#53411yescharacteristic
366C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C151#57511yescharacteristic
370C4×C151—22no—
371C4×C151—22no—
372C4×C151—41no—
373C4×C151—44no—
374C4×C151—81no—
375C4×C151—81no—
376C4×C151—81no—
377C4×C151D4212yes—
378C4×C151#54612yes—
379C2×C151—24no—
380C2×C151—42no—
381C2×C151—42no—
382C2×C151—84no—
383C2×C151—161no—
384C2×C151#241011yescharacteristic
385C2×C151#300311yescharacteristic
386C2×C151#300611yescharacteristic
387C2×C151C2×#46911yescharacteristic
388C2×C151#305511yescharacteristic
389C2×C151#319211yescharacteristic
390C2×C151#319411yescharacteristic
391#24384C15111yesmaximal, characteristic, direct product factor, Sylow
392C151#2438411yescharacteristic, direct product factor, Sylow
393C22×#121C2×C15111yescharacteristic, complemented
394C2×#469C2×C15112yescomplemented
395C2×#447C2×C15111yescharacteristic, complemented
396C2×#407C2×C15111yescharacteristic, complemented
397#2847C2×C15111yescharacteristic, complemented
398#2034C2×C15112yescomplemented
399#1999C2×C15112yescomplemented
400#1895C2×C15112yescomplemented
401#1874C2×C15111yescharacteristic, complemented
402#1853C2×C15111yescharacteristic, complemented
403#1786C2×C15111yescharacteristic, complemented
404C23×D4—21no—
405C23×D4C22×C15111yescharacteristic
406C24×C4C22×C15111yescharacteristic
407C22×D8C22×C15112yescomplemented
408C22×M16C22×C15112yescomplemented
409C2×#121—21no—
410C2×#121—21no—
411C2×#121—28no—
412C2×#121C22×C15111yescharacteristic
413C2×#121C22×C15112yes—
414C2×#121C22×C15112yes—
415C2×#121C22×C15111yescharacteristic, complemented
416C2×#121C22×C15111yescharacteristic, complemented
417C2×#120—21no—
418C22×C4⋊C4C22×C15111yescharacteristic
419C22×C22⋊C4—21no—
420#469—28no—
421#447—24no—
422C2×#106C22×C15112yescomplemented
423C2×#102C22×C15112yescomplemented
424C2×#102C22×C15112yescomplemented
425C2×#102C22×C15112yescomplemented
426C2×#102C22×C15112yescomplemented
427#407—24no—
428C2×C22⋊C8C22×C15111yescharacteristic
429C2×C22⋊C8C22×C15111yescharacteristic
430C2×C22⋊C8C22×C15112yescomplemented
431#386—21no—
432#386—21no—
433#386—21no—
434#380C22×C15111yescharacteristic
435#380C22×C15111yescharacteristic, complemented
436#380C22×C15111yescharacteristic, complemented
437#340C22×C15112yescomplemented
438#340C22×C15112yescomplemented
439C25—21no—
440C25D4×C15111yescharacteristic
441C22×D4—28no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—22no—
451C22×D4—42no—
452C22×D4—44no—
453C22×D4—44no—
454C22×D4C23×C15111yescharacteristic
455C22×D4C23×C15112yes—
456C23×C4—21no—
457C23×C4—22no—
458C23×C4—24no—
459C23×C4—22no—
460C23×C4—42no—
461C23×C4D4×C15111yescharacteristic
462C23×C4D4×C15111yescharacteristic
463C23×C4D4×C15111yescharacteristic
464C23×C4C23×C15111yescharacteristic
465C23×C4C23×C15111yescharacteristic
466C23×C4C23×C15111yescharacteristic
467C2×D8—24no—
468C2×D8—24no—
469C2×D8—42no—
470C2×M16—24no—
471C2×M16—24no—
472C2×M16—42no—
473C22×C8C23×C15112yes—
474C22×C8C23×C15112yes—
475#121—28no—
476#121—28no—
477#121—24no—
478#121—24no—
479#121—24no—
480#121—22no—
481#121—22no—
482#121—24no—
483#121—42no—
484#121D4×C15118yescomplemented
485#120—44no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4C23×C15111yescharacteristic
489C2×C4⋊C4C23×C15111yescharacteristic
490C2×C4⋊C4C23×C15111yescharacteristic
491C2×C4⋊C4C23×C15112yes—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501#106—24no—
502#102—24no—
503#102—24no—
504#102—24no—
505#102—42no—
506C22⋊C8—22no—
507C22⋊C8—24no—
508C22⋊C8D4×C15114yescomplemented
509#95—21no—
510#95—21no—
511#95—21no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—24no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24—41no—
521C24—41no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24—42no—
528C24C2×D4×C15111yescharacteristic
529C24C2×D4×C15111yescharacteristic
530C24C2×D4×C15111yescharacteristic
531C2×D4—24no—
532C2×D4—28no—
533C2×D4—28no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—42no—
546C2×D4—432no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4C2×D4×C15114yes—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4C2×D4×C15111yescharacteristic
590C22×C4C2×D4×C15111yescharacteristic
591C22×C4C2×D4×C15114yes—
592C22×C4C2×D4×C15111yescharacteristic
593C22×C4C2×D4×C15112yes—
594C22×C4#41×C15112yes—
595C22×C4C24×C15111yescharacteristic
596D8—48no—
597M16—48no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8C2×D4×C15114yescomplemented
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4C2×D4×C15114yes—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—28no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—24no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—48no—
643C23—48no—
644C23—48no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—84no—
660C23—84no—
661C23—84no—
662C23—84no—
663C23#120×C15112yes—
664C23#121×C15112yes—
665C23AGL(1,ℤ/8)×C15112yes—
666C23AGL(1,ℤ/8)×C15112yes—
667C23AGL(1,ℤ/8)×C15112yes—
668C23C22×D4×C15111yescharacteristic
669D4—24no—
670D4—24no—
671D4—48no—
672D4—416no—
673D4—416no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—84no—
679D4—84no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—21no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4#120×C15112yes—
711C2×C4#121×C15112yes—
712C2×C4C22×D4×C15111yescharacteristic
713C2×C4C22×D4×C15112yes—
714C2×C4C2×#41×C15111yescharacteristic
715C2×C4H(5,𝔽2)×C15112yes—
716C8—24no—
717C8—42no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—416no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—816no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22#469×C15114yescomplemented
755C22C2×#120×C15111yescharacteristic
756C22C2×#121×C15111yescharacteristic
757C22#534×C15111yescharacteristic
758C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
759C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
760C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
761C22#575×C15111yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—44no—
766C4—81no—
767C4—81no—
768C4—81no—
769C4D42×C15112yes—
770C4#546×C15112yes—
771C2—24no—
772C2—42no—
773C2—42no—
774C2—84no—
775C2—161no—
776C2#2410×C15111yescharacteristic
777C2#3003×C15111yescharacteristic
778C2#3006×C15111yescharacteristic
779C2C2×#469×C15111yescharacteristic
780C2#3055×C15111yescharacteristic
781C2#3192×C15111yescharacteristic
782C2#3194×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#121×C151C2semidirect
2. C2×#469×C151C2semidirect
3. C2×#447×C151C2semidirect
4. C2×#407×C151C2semidirect
5. #2847×C151C2semidirect
6. #2034×C151C2semidirect
7. #1999×C151C2semidirect
8. #1895×C151C2semidirect
9. #1874×C151C2semidirect
10. #1853×C151C2semidirect
11. #1786×C151C2semidirect
15. C22×D8×C151C22semidirect
16. C22×M16×C151C22semidirect
23. C2×#121×C151C22semidirect
24. C2×#121×C151C22semidirect
30. C2×#106×C151C22semidirect
31. C2×#102×C151C22semidirect
32. C2×#102×C151C22semidirect
33. C2×#102×C151C22semidirect
34. C2×#102×C151C22semidirect
38. C2×C22⋊C8×C151C22semidirect
43. #380×C151C22semidirect
44. #380×C151C22semidirect
45. #340×C151C22semidirect
46. #340×C151C22semidirect
92. #121×C151D4semidirect
116. C22⋊C8×C151D4semidirect
211. C2×C8×C151C2×D4semidirect
362. C22×C151#469semidirect
391. #24384C151direct (N × H)
392. C151#24384direct (N × H)
393. C22×#121C2×C151semidirect
394. C2×#469C2×C151semidirect
395. C2×#447C2×C151semidirect
396. C2×#407C2×C151semidirect
397. #2847C2×C151semidirect
398. #2034C2×C151semidirect
399. #1999C2×C151semidirect
400. #1895C2×C151semidirect
401. #1874C2×C151semidirect
402. #1853C2×C151semidirect
403. #1786C2×C151semidirect
407. C22×D8C22×C151semidirect
408. C22×M16C22×C151semidirect
415. C2×#121C22×C151semidirect
416. C2×#121C22×C151semidirect
422. C2×#106C22×C151semidirect
423. C2×#102C22×C151semidirect
424. C2×#102C22×C151semidirect
425. C2×#102C22×C151semidirect
426. C2×#102C22×C151semidirect
430. C2×C22⋊C8C22×C151semidirect
435. #380C22×C151semidirect
436. #380C22×C151semidirect
437. #340C22×C151semidirect
438. #340C22×C151semidirect
484. #121D4×C151semidirect
508. C22⋊C8D4×C151semidirect
603. C2×C8C2×D4×C151semidirect
754. C22#469×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#121×C1512
C2×#469×C1512
C2×#447×C1512
C2×#407×C1512
#2847×C1512
#2034×C1512
#1999×C1512
#1895×C1512
#1874×C1512
#1853×C1512
#1786×C1512
#24384151